From what I read Mexica arrived late to those territories and simply couldn’t get better land. In the end they got lucky. They were not able to grow enough food on the island so fish, birds and eggs formed big part of their diet. This made their warriors better at doing warrior things for reasons we’re not sure about. Maybe it was because they were not tied to farming calendar as much or maybe it was the extra protein. They eventually conquered all the neighboring tribes and built a nice city on that island.